Singularity of projections of 2-dimensional measures invariant under the geodesic flow

We show that on any compact Riemann surface with variable negative curvature there exists a measure which is invariant and ergodic under the geodesic flow and whose projection to the base manifold is 2-dimensional and singular with respect to the 2-dimensional Lebesgue measure.Comment: 12 page

Visible parts of fractal percolation

We study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditioned on non-extinction, almost surely all visible parts from lines are 1-dimensional. Furthermore, almost all of them have positive and finite Hausdorff measure. We also verify analogous results for visible parts from points. These results are motivated by an open problem on the dimensions of visible parts.Comment: 22 pages, 3 figure

Hausdorff dimension of affine random covering sets in torus

We calculate the almost sure Hausdorff dimension of the random covering set $\limsup_{n\to\infty}(g_n + \xi_n)$ in $d$-dimensional torus $\mathbb T^d$, where the sets $g_n\subset\mathbb T^d$ are parallelepipeds, or more generally, linear images of a set with nonempty interior, and $\xi_n\in\mathbb T^d$ are independent and uniformly distributed random points. The dimension formula, derived from the singular values of the linear mappings, holds provided that the sequences of the singular values are decreasing.Comment: 16 pages, 1 figur

Report on Organic Food and Farming in Finland

The interest in research on organic farming grew in the beginning of the 1980s. In 1980, an extensive seven-year-project started in cooperation between several institutions investigating the possibility to improve the efficiency of nitrogen fixation and utilisation of nitrogen fertilisers and cow manure. Two extensive comparative projects began in 1982: (1) conventional and organic cropping systems at Suitia, University of Helsinki and (2) self-sufficient crop rotation and cropping system by the Agricultural Research Centre of Finland at its regional research stations. In September 1985, the Partala Centre for Rural Development for research on organic farming was founded in Juva. The University of Helsinki, Juva municipality and some other organisations belonged to this Partala association, as it is called nowadays. Partala experimental farm was integrated into the MTT Agricultural Research Centre of Finland in 1990. MTT Partala and Karila in nearby town Mikkeli were joined together in 1996 to the MTT Research Station of Ecological Production. Partala research station and later MTT/Ecological Production has coordinated research on Organic Food and Farming in Finland since 1990. It has launched three research programmes, which have covered the whole organic sector from soil issues to food processing and markets, as well as social issues. Professor Artur Granstedt from Sweden was nominated as professor for organic farming research in Partala for 5 years in 1993, and he influenced strongly the research programmes of Organic Food and Farming at that time. MTT Ecological Production established ‘The Finnish Research Network on Organic Agri-Food Systems’ (ReNOAF), together with other stakeholders in 2000 and has coordinated this network ever since. Funding directed especially for research programmes on Organic Food and Farming (OF&F) was addressed for the first time in Finland in 2003, when the Ministry of Agriculture and Forestry launched its first research programme on Organic Food and Farming, based on the priorities prepared in the ReNOAF. National research seminars were also organised by MTT Ecological Production. The Partala Research Station will be closed down in September 2006. The lands of the Partala Research Station will remain under organic farming research, but all personnel will move to the Mikkeli Research Station to work in close connection with the Ruralia Institute of the University of Helsinki. The reason for this decision was to improve efficiency by having a better critical mass of researchers by putting more people to work together and by concentrating the resources. At the University of Helsinki, the Mikkeli Institute for Rural Research and Training (Ruralia Institute Mikkeli Unit), a neighbour of MTT Ecological Production, got started in 1988. Organic production has been one of its priorities from the very beginning. It has concentrated on further training and development activities. It has, for example, educated all advisors and teachers for organic farming since 1991. Developing activities have covered the processing and marketing of food, plant protection and animal welfare. In 2000, the only academic educational programme for Organic Food and Farming was started there. This Eco Studies – project has been under way at the Ruralia Institute Mikkeli Unit of the University of Helsinki since 2001. The project consists of scientific research and university level study entities. Studies in the organic agri-food systems study programme are available for university students and through the Open University for all who are interested in the field. It provides opportunities to join the European and Nordic study programmes, too. Organic production, marketing and consumption of organic products are also studied in Finland at the other departments of the MTT Agrifood Research and University of Helsinki, the University of Joensuu, the National Consumer Research Centre, the VTT Technical Research Centre, the National Veterinary and Food Research Institute and the Work Efficiency Institute

Dimensions of random affine code tree fractals

We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.Comment: 22 page

Packing-Dimension Profiles and Fractional Brownian Motion

In order to compute the packing dimension of orthogonal projections Falconer and Howroyd (1997) introduced a family of packing dimension profiles ${\rm Dim}_s$ that are parametrized by real numbers $s>0$. Subsequently, Howroyd (2001) introduced alternate $s$-dimensional packing dimension profiles \hbox{{\rm P}$-$\dim}_s and proved, among many other things, that \hbox{{\rm P}$-$\dim}_s E={\rm Dim}_s E for all integers $s>0$ and all analytic sets $E\subseteq\R^N$. The goal of this article is to prove that \hbox{{\rm P}$-$\dim}_s E={\rm Dim}_s E for all real numbers $s>0$ and analytic sets $E\subseteq\R^N$. This answers a question of Howroyd (2001, p. 159). Our proof hinges on a new property of fractional Brownian motion